Is it true that given a fusion category $\mathcal{C}$ and its Drinfel'd center $Z(\mathcal{C})$, there is a fully faithful functor $F:\mathcal{C}\hookrightarrow Z(\mathcal{C})$? I.e. can $\mathcal{C}$ can be identified with a full monoidal subcategory of $Z(\mathcal{C})$?

Judging by the mention of a 'restriction functor' $Z(\mathcal{C})\to\mathcal{C}$ here, the answer would be yes -- but are there any references for this result in the literature? Thanks!